Abstract [en]

The SVI implied volatility model is a parametric model for stochastic implied volatility.The SVI is interesting because of the possibility to state explicit conditions on its parameters so that the model does not generate prices where static arbitrage opportunities can occur. Calibration of the SVI model to real market data requires non-linear optimization algorithms and can be quite time consuming. In recent years, methods to calibrate the SVI model that use its inherent structure to reduce the dimensions of the optimization problem have been invented in order to speed up the calibration. The ?first aim of this thesis is to justify the use of the model and the no static arbitrage conditions from a theoretic point of view. Important theorems by Kellerer and Lee and their proofs are discussed in detail and the conditions are carefully derived. The second aim is to implement the model so that it can be calibrated to real market implied volatility data. A calibration method is presented and the outcome of two numerical experiments validate it. The performance of the calibration method introduced in this thesis is measured in how big a fraction of the total market volume the method manages to ?t within the market spread. Tests show that the model manages to ?t most of the market volume inside the spread, even for options with short time to maturity. Further tests show that the model is capable to recalibrate an SVI parameter set that allows for static arbitrage opportunities into an SVI parameter set that does not.